Brice Magdalou (University of Montpellier) on Ranking Distributions of an Ordinal Attribute

This paper establishes an equivalence between three incomplete rank- ings of distributions of an ordinally measurable attribute. The first rank- ing is that associated with the possibility of going from distribution to the other by a finite sequence of two elementary operations: increments of the attribute and the so-called Hammond transfer. The later transfer is like the Pigou-Dalton transfer, but without the requirement - that would be senseless in an ordinal setting - that the "amount" transferred from the "rich" to the "poor" is fixed. The second ranking is an easy-to-use statistical criterion associated to a specifically weighted recursion on the cumulative density of the distribution function. The third ranking is that resulting from the comparison of numerical values assigned to distribu- tions by a large class of additively separable social evaluation functions. Illustrations of the criteria are also provided.